Most of the CFD codes on the market today feature a powerful algebraic solver based on multigrid acceleration. It could be argued that the multigrid solver is the single greatest innovation in CFD. Because of the large models routinely encountered, CFD developers quickly realized that direct solvers were too memory intensive and turned to iterative solvers. However, iterative solvers, while memory efficient, are notoriously slow. The multigrid acceleration technique speeds up iterative solvers tremendously allowing for realistic CFD models which otherwise would not be feasible on today's computers.

In this article, I will attempt to explain just how the multigrid method achieves these remarkable results.